Question

Suppose a soccer goalie punted the ball in such a way as to kick the ball as far as possible down the field. The height of the ball above the field can be approximated by the function below where y represents the height of the ball (in yards) and x represents the horizontal distance (in yards) down the field from where the goalie kicked the ball.
`y=0.017x^(2) +0.98x+0.33`

How far away did the ball land? Estimate to 2 places after the decimal.

Answer 1

57.98 yards

Explanation:

When the ball is on the ground, the height is
`y=0`, therefore:

`y=-0.017x^2+0.98x+0.33`

`0=-0.017x^2+0.98x+0.33`

`x=(-b\pm√(b^2-4ac))/(2a)`

`x=(-0.98\pm√(0.98^2-4(-0.017)(0.33)))/(2(-0.017))`

`x_1=57.98184919`

`x_2=-0.3347903693`

Since distance cannot be negative, the ball landed 57.98 yards down the field from where the goalie kicked the ball.